Rate and Noise-Induced Tipping Working in Concert

TL;DR

This paper investigates how noise influences rate-induced tipping in dynamical systems, revealing that noise can trigger tipping at lower rates than expected, with the most probable paths characterized through large deviation theory.

Contribution

It demonstrates that noise can induce tipping below the critical rate and identifies the most probable tipping paths using Freidlin-Wentzell theory.

Findings

Noise lowers the critical rate for tipping.

Most probable paths are heteroclinic connections.

Monte Carlo simulations confirm theoretical predictions.

Abstract

Rate-induced tipping occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states. We show that the addition of noise to the system can cause it to tip well below the critical rate at which rate-induced tipping would occur. Moreover it does so with significantly increased probability over the noise acting alone. We achieve this by finding a global minimizer in a canonical problem of the Freidlin-Wentzell action functional of large deviation theory that represents the most probable path for tipping. This is realized as a heteroclinic connection for the Euler-Lagrange system associated with the Freidlin-Wentzell action and we find it exists for all rates less than or equal to the critical rate. Its role as most probable path is corroborated by direct Monte Carlo simulations.